The brain includes gray matter connected by channels of white matter, sometimes referred to as fiber bundles, or fasciculi. A purpose of tractography is to identify the paths followed by the white matter, to use those paths to form a normative map of a fully functional brain and to detect differences between functional and dysfunctional brains.
A physiological characteristic of the white matter tracks is that hydrogen protons attached to water molecules in the cerebrospinal fluid will tend to diffuse along the direction of those tracks. Thus, by observing the directions in which water diffuses at different locations in the brain, one can identify the directions of major fiber bundles within the brain tissue. The preferred direction of diffusion, and the extent of that preference, can be described by a tensor field. Thus, if one could evaluate the diffusion tensor at each point in the brain tissue, one would be able to determine the directions of the fiber bundles in that tissue.
One technique of tractography is to use diffusion tensor magnetic resonance imaging (“DT-MRI”) to observe the diffusion of water in brain tissue. Using those observations, one can infer the value of the diffusion tensor at different locations in that tissue.
To reduce the likelihood that anomalies in a single subject will skew the resulting measurements, imaging is carried out on a large number of subjects. Data obtained from the subjects is then averaged across all subjects. In principle, this technique will average out differences between subjects.
One difficulty with this approach is that it is almost impossible to ensure that the brains of two different subjects are perfectly aligned during the MRI data collection period. In fact, even if one were to take two measurements of the same subject, one might obtain two different results, simply because the location of the subject's head in the MRI machine may not be identical for both measurements.
Thus, variation between measurements can arise from several causes. First, variations may arise from the anatomical differences between patients. These are among the variations that are to be averaged out. However, variations may also arise from poor “registration” (i.e. alignment of images) between subjects. These variations have no anatomical significance and will therefore tend to corrupt any estimate of the diffusion tensor. Additional sources of variation having no anatomical significance include machine noise (for example, eddy currents, RF noise, or noise in the hardware) and physiological noise (for example, artifacts, cardiac pulsation, and magnetic susceptibility). These noise sources add to variation across subjects.